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What does capacitor impedance/ESR frequency characteristic mean?
This column is a technical column explaining capacitor foundation.
The frequency characteristics of capacitor impedance | Z | and equivalent series resistance (ESR) are described.
By understanding the frequency characteristics of capacitors, we can judge the ability of power lines to eliminate noise and suppress voltage fluctuation, which can be said to be an indispensable important parameter in circuit design. Impedance magnitude | Z | and ESR in frequency characteristics are described here.
1. Frequency characteristics of capacitors
If the angular frequency is assumed to be_and the static capacity of the capacitor to be C, then the impedance Z of the capacitor (Fig. 1) in the ideal state can be formulated.
(1) Representation.
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Figure 1. Ideal capacitor
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It can be seen from formula (1) that the impedance | Z | decreases in inverse proportion to frequency as shown in figure 2. Because there is no loss in the ideal capacitor, the equivalent series resistance (ESR) is zero.
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Figure 2. Frequency characteristics of ideal capacitors
But in the actual capacitor (Figure 3), besides the capacity component C, there are also resistance (ESR) and parasitic inductance (ESL) generated by dielectric or electrode loss. Therefore, the frequency characteristics of | Z | are V-shaped (some capacitors may change to U-shaped) as shown in Figure 4, and ESR also shows the frequency characteristics corresponding to the loss value.
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Figure 3. Actual capacitors
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Figure 4. Frequency characteristics of | Z |/ ESR for practical capacitors (example)
| The reasons why Z | and ESR became the curve in Figure 4 are as follows.
Low Frequency Range: Low Frequency Range | Z | is the same as the ideal capacitor, and decreases in inverse proportion to the frequency. ESR values also show the characteristics corresponding to dielectric loss caused by dielectric polarization delay.
Near the resonance point: | Z | will be affected by ESR produced by parasitic inductance or specific resistance of electrodes, deviating from the ideal capacitor (red dotted line), showing the minimum value. | The frequency at which Z | is the minimum is called the natural frequency, and then | Z |= ESR. If the frequency is larger than the natural frequency, the component characteristics will change from capacitor to inductor and | Z | will increase. The range below the natural frequency is called the capacitive domain, and vice versa is called the perceptual domain.
ESR is affected not only by dielectric loss, but also by the loss of resistance travel of the electrode itself.
High frequency range: The characteristics of | Z | in the high frequency range above the resonance point are determined by the parasitic inductance (L). The high frequency range | Z | can be approximated by formula (2) and increases in direct proportion to frequency.
ESR gradually showed the skin effect and proximity effect of electrodes.
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These are the frequency characteristics of actual capacitors. Importantly, the higher the frequency, the less we can ignore the effects of ESR or ESL. With the increasing application of capacitors in the high frequency field, ESR and ESL, like the static capacitance value, become important parameters to represent the performance of capacitors.
2. Frequency Characteristics of Various Capacitors
The great influence of parasitic components ESR and ESL on frequency characteristics of capacitors is described above. The parasitic component varies with the type of capacitor. Next, the differences of frequency characteristics of different types of capacitors are explained.
Fig. 5 shows the frequency characteristics of | Z | and ESR of various capacitors with electrostatic capacity of 10uF. Except for thin film capacitors, all are SMD capacitors.
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Figure 5. Frequency characteristics of | Z |/ ESR for various capacitors
The electrostatic capacitance values of the capacitors shown in Fig. 5 are all 10uF, so the capacitance range | Z | with frequencies less than 1kHz is the same. However, | Z | of aluminium electrolytic capacitors or tantalum electrolytic capacitors is larger than that of multi-layer ceramic capacitors or thin film capacitors when the specific resistance of electrolyte materials of aluminium electrolytic capacitors or tantalum electrolytic capacitors is higher than that of thin film capacitors, which leads to the increase of ESR. Metal materials are used in the electrodes of thin film capacitors or multilayer ceramic capacitors, so ESR is very low.
The characteristics of multi-layer ceramic capacitors and pin-type thin film capacitors are basically the same near the resonance point, but the self-vibration frequency of multi-layer ceramic capacitors is high and the inductance range | Z | is low. This is because the inductance of the pin-line part of the pin-type thin film capacitor increases.
From the above results, it can be concluded that SMD multilayer ceramic capacitors have low impedance in a wide frequency range and are most suitable for high frequency applications.
3. Frequency Characteristics of Multilayer Ceramic Capacitors
Multilayer ceramic capacitors can be classified into many types according to their raw materials and shapes. Following is a description of the effects of these factors on frequency characteristics.
(1) About ESR
ESR in the field of capacitance is determined by dielectric loss produced by dielectric materials. Class2 (Category 2) materials with high dielectric rate tend to increase ESR due to the use of strong dielectrics. Class 1 (Category 1) temperature compensation material has very small dielectric loss and ESR value due to the use of general dielectrics.
ESR in high frequency field from resonance point to inductive field is affected not only by specific resistivity of electrode material, shape of electrode (thickness, length, width), number of layers, but also by skin effect or proximity effect. Electrode materials mostly use Ni, but in low-loss capacitors, copper with lower specific resistivity is sometimes used as electrode materials.
(2) About ESL
ESL of multilayer ceramic capacitors is very susceptible to the influence of internal electrode structure. When the length, width and thickness of the inner electrode are l, W and d, according to F. W. Grover, the ESL of the electrode inductance can be expressed by formula (3).
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From this formula, we can know that the shorter, wider and thicker the electrodes of capacitors, the smaller the ESL.
Figure 6 shows the relationship between rated capacitance and natural frequency of multi-layer ceramic capacitors with different sizes.